This example demonstrates how to create a neuronal ensemble that will combine two 1-D inputs into one 2-D representation.

In [1]:
import matplotlib.pyplot as plt
%matplotlib inline

import nengo

Step 1: Create the neural populations

Our model consists of three ensembles, two input ensembles and one 2-D ensemble that will represent the two inputs as one two-dimensional signal.

In [2]:
model = nengo.Network(label='Combining')
with model:
    # Our input ensembles consist of 100 leaky integrate-and-fire neurons,
    # representing a one-dimensional signal
    A = nengo.Ensemble(100, dimensions=1)
    B = nengo.Ensemble(100, dimensions=1)

    # The output ensemble consists of 200 leaky integrate-and-fire neurons,
    # representing a two-dimensional signal
    output = nengo.Ensemble(200, dimensions=2, label='2D Population')

Step 2: Create input for the model

We will use sine and cosine waves as examples of continuously changing signals.

In [3]:
import numpy as np
with model:
    # Create input nodes generating the sine and cosine
    sin = nengo.Node(output=np.sin)
    cos = nengo.Node(output=np.cos)

Step 3: Connect the network elements

In [4]:
with model:
    nengo.Connection(sin, A)
    nengo.Connection(cos, B)

    # The square brackets define which dimension the input will project to
    nengo.Connection(A, output[1])
    nengo.Connection(B, output[0])

Step 4: Probe outputs

Anything that is probed will collect the data it produces over time, allowing us to analyze and visualize it later.

In [5]:
with model:
    sin_probe = nengo.Probe(sin)
    cos_probe = nengo.Probe(cos)
    A_probe = nengo.Probe(A, synapse=0.01)  # 10ms filter
    B_probe = nengo.Probe(B, synapse=0.01)  # 10ms filter
    out_probe = nengo.Probe(output, synapse=0.01)  # 10ms filter

Step 5: Run the model

In [6]:
# Create our simulator
with nengo.Simulator(model) as sim:
    # Run it for 5 seconds

Step 6: Plot the results

In [7]:
# Plot the decoded output of the ensemble
plt.plot(sim.trange(),[out_probe][:, 0], 'b', label="2D output")
plt.plot(sim.trange(),[out_probe][:, 1], 'g', label="2D output")
plt.plot(sim.trange(),[A_probe], 'r', label="A output")
plt.plot(sim.trange(),[sin_probe], 'k', label="Sine")
<matplotlib.legend.Legend at 0x7f4794967c88>

The graph shows that the input signal (Sine), the output from the 1D population (A output), and the 2D population (green line) are all equal. The other dimension in the 2D population is shown in blue.